Let's say we model an OIS short rate process with the Hull-White one-factor model, and there is one OIS short rate process for each currency. From what I gather, usually the correlations between short rate processes are estimated using historical data. The question is what historical data we should you, given that short rates are not observable. I intended to use overnight rates, such as Fed fund rate, Eonia, etc. However, some people argue that we'd better use OIS swap rates with a maturity of, say, 30 years, to estimate the correlation matrix. Are OIS swap rates a good proxy for OIS short rates? What data would you use?